To some extent you have a right to the name if you used it first and if you registered it as a fictitious business name.
If somehow the use of the name on the account could result in confusion between the two businesses, then maybe you could get an injunction against the person to stop using the name. You could also possibly get damages if the use of the name in any way cost you money.
However, to give a definite answer to your question, a person would have to know a lot more facts in the situation. Therefore, if this is a serious problem, I suggest you consult an Intellectual property attorney, and perhaps have the attorney write a letter on your behalf.